Alimon, Nur Idayu and Sarmin, Nor Haniza and Erfanian, Ahmad
(2023)
*On the Szeged index and its non-commuting graph.*
Jurnal Teknologi, 85
(3).
pp. 105-110.
ISSN 0127-9696

PDF
410kB |

Official URL: http://dx.doi.org/10.11113/jurnalteknologi.v85.192...

## Abstract

In chemistry, the molecular structure can be represented as a graph. Based on the information from the graph, its characterization can be determined by computing the topological index. Topological index is a numerical value that can be computed by using some algorithms and properties of the graph. Meanwhile, the non-commuting graph is a graph, in which two distinct vertices are adjacent if and only if they do not commute, where it is made up of the non-central elements in a group as a vertex set. In this paper, the Szeged index of the non-commuting graph of some finite groups are computed. This paper focuses on three finite groups which are the quasidihedral groups, the dihedral groups, and the generalized quaternion groups. The construction of the graph is done by using Maple software. In finding the Szeged index, some of the previous results and properties of the graph for the quasidihedral groups, the dihedral groups, and the generalized quaternion groups are used. The generalisation of the Szeged index of the non-commuting graph is then established for the aforementioned groups. The results are then applied to find the Szeged index of the non-commuting graph of ammonia molecule.

Item Type: | Article |
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Uncontrolled Keywords: | dihedral groups, generalized quaternion groups, non-commuting graph, quasidihedral groups, Szeged index |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 105182 |

Deposited By: | Yanti Mohd Shah |

Deposited On: | 07 Apr 2024 04:14 |

Last Modified: | 07 Apr 2024 04:14 |

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